Thermodynamic States of the Mixed Spin 1/2 and Spin 1 Hexagonal Nanowire System Obtained from a Seven-Site Cluster Within an Improved Mean Field Approximation

The mean field approximation results in the mixedspin 1/2 Ising model and spin 1 Blume-Capel model, in the hexagonal nanowire system, are obtained from the Bogoliubov inequality. The Gibbs free energy, magnetization, and critical frontiers are obtained. Besides the stable branches of the order parameters, we obtain the metastable and unstable parts of these curves and also find phase transitions of the metastable branches of the order parameters. The classification of the stable, metastable, and unstable states is made by comparing the free energy values of these states.     

An effective-field theory study of hexagonal Ising nanowire: Thermal and magnetic properties

By means of the effective-field theory （EFT） with correlations, the thermodynamic and magnetic quantities （such as magnetization, susceptibility, internal energy, specific heat, free energy, hysteresis curves, and compensation behaviors） of the spin-l/2 hexagonal Ising nanowire （HIN） system with core/shell structure have been presented. The hysteresis curves are obtained for different values of the system parameters, in both ferromagnetic and antiferromagnetic cases. It has been shown that the system only undergoes a second-order phase transition. Moreover, from the thermal variations of the total magnetization, the five compensation types can be found under certain conditions, namely the Q-, R-, S-, P-, and N-types.     

Exact solution of the spin-1/2 Ising model on the Shastry–Sutherland (orthogonal-dimer) lattice

A star-triangle mapping transformation is used to establish an exact correspondence between the spin-1/2 Ising model on the Shastry–Sutherland (orthogonal-dimer) lattice and respectively, the spin-1/2 Ising model on a bathroom tile (4–8) lattice. Exact results for the critical temperature and spontaneous magnetization are obtained and compared with corresponding results on the regular Ising lattices.     

Microcanonical Phase Diagram of the BEG and Ising Models

The density of states of long-range Blume-Emery-Griffiths (BEG) and short-range Ising models are obtained by using Wang-Landau sampling with adaptive windows in energy and magnetization space. With accurate density of states, we are able to calculate the microcanonical specific heat of fixed magnetization introduced by Kastner et al. in the regions of positive and negative temperature. The microcanonical phase diagram of the Ising model shows a continuous phase transition at a negative temperature in energy and magnetization plane. However the phase diagram of the long-range model constructed by peaks of the microcanonical specific heat looks obviously different from the Ising chart.     

Microcanonical Phase Diagram of the BEG and Ising Models

The density of states of long-range Blume-Emery-Griffiths(BEG) and short-range Ising models are obtained by using Wang-Landau sampling with adaptive windows in energy and magnetization space.With accurate density of states,we are able to calculate the microcanonical specific heat of fixed magnetization introduced by Kastner et al.in the regions of positive and negative temperature.The microcanonical phase diagram of the Ising model shows a continuous phase transition at a negative temperature in energy and magnetization plane.However the phase diagram of the long-range model constructed by peaks of the microcanonical specific heat looks obviously different from the Ising chart.     

稀释晶场对纳米管上Blume-Capel模型磁化性质的研究

利用有效场理论研究了纳米管上稀释晶场中Blume-Capel模型格点的磁化强度、内能、比热和自由能,得到了系统格点的磁化强度、内能、比热和自由能与温度和稀释晶场的关系.结果表明:稀释晶场取值概率和晶场强度等诸多因素相互竞争,使系统表现出比含恒定晶场作用的Blume-Capel模型更为丰富的磁学特性;稀释晶场会抑制系统格点的磁化强度,导致其基态饱和值小于1;温度较低时,系统格点的磁化强度表现出复杂性;晶场较强时,系统的内能、比热和自由能也呈现出不同的磁学性质.     

An effective-field study of Ising metamagnet in an external field

The phase diagrams and magnetization curves of a two-sublattice Ising metamagnet at finite temperature with longitudinal crystal field H are investigated by the use of an effective-field theory (EFT) with correlations. In addition to the second-order transition lines, the first-order transition lines are also presented, since a method to calculate the Gibbs free energy numerically at finite temperature within EFT is found in this work. The results show that there is no fourth-order critical point or reentrant phenomenon in the phase diagrams given by using EFT as found by using mean-field theory (MFT).     

Magnetic properties in a transverse Ising nanowire with an antiferromagnetic spin configuration at the surface

The phase diagrams and temperature dependences of magnetizations in a transverse Ising nanowire with an antiferromagnetic spin configuration at the surface are studied by the use of the effective-field theory with correlations. A number of characteristic features, such as the possibility of reentrant phenomena being free from disorder-induced frustration, are obtained for the magnetic properties in the system.     

Critical phenomena at edges and corners

Using Monte-Carlo techniques, the critical behaviour at edges and corners of the three-dimensional Ising model is studied. In particular, the critical exponent of the local magnetization at edges formed by two intersecting free surfaces is estimated to be, as a function of the opening angle , for , for , and for . The critical exponent of the corner magnetization of a cube is found to be . The Monte-Carlo estimates are compared to results of mean field theory, renormalization group calculations and high temperature series expansions. Received: 29 January 1998 / Accepted: 17 March 1998     

Hysteresis behaviors in a cylindrical Ising nanowire

The hysteresis behaviors of the cylindrical Ising nanowire are investigated within the effective-field theory with correlations at temperatures below, around and above the critical temperature. The hysteresis curves are obtained for different reduced temperatures both ferromagnetic and antiferromagnetic interactions between the shell and the core. We find that the hysteresis loop areas decrease when the reduced temperatures increase, and the hysteresis loops disappear at certain reduced temperatures. Moreover, for the antiferromagnetic nanowire the hysteresis loop areas disappear earlier than the ferromagnetic case as the reduced temperature increases. An unusual form of triple hysteresis behaviors is observed for the antiferromagnetic nanowire system. The thermal behaviors of the coercivities and remanent magnetizations are also investigated. The results are in good agreement with some experimental and theoretical results.     

Ordering in Ising models of parabolic shape

The features of order in narrow systems are studied for isotropic square lattice Ising models with general parabolic boundaries. Using Monte Carlo methods, magnetization profiles are calculated which agree very well with the conformal results and scale properly with the geometrical length parameter. The variation of the tip magnetization with temperature is obtained and the predicted stretched exponential form in the critical region is confirmed.     

Two distinct magnetic susceptibility peaks and magnetic reversal events in a cylindrical core/shell spin-1 Ising nanowire

The magnetization and susceptibility of a cylindrical core/shell spin-1 Ising nanowire are investigated within the effective-field theory with correlations for both ferromagnetic and antiferromagnetic exchange interactions between the shell and the core. We find that the nanowire system exhibits two distinct susceptibility peaks and two successive phase transitions; either both of them are second-order transitions or one is a second-order transition and the other is a first-order transition for a small exchange interaction. The susceptibility versus switching field and the hysteresis behavior are investigated for different temperatures. It is found that the magnetization reversal events appear as peaks in the susceptibility versus switching field curve, the positions of which define the coercive field points of the nanowire system; the distance between the two susceptibility peaks decreases with increasing temperature.     

外磁场对纳米管上Blume-Capel模型磁热性能的研究

利用有效场理论研究了纳米管上外磁场中Blume-Capel模型格点的磁化强度、磁化率、内能、比热和自由能,得到了系统格点的磁化强度、磁化率、内能、比热和自由能与外磁场和晶场的关系.结果表明:外磁场强度、交换相互作用和晶场强度等诸多因素相互竞争,使系统表现出比没有外磁场作用的Blume-Capel模型更为丰富的磁学特性;外磁场能够增大系统格点的磁化强度,导致系统的二级相变消失;负晶场作用系统时,系统会发生一级相变;晶场强度、外磁场强度不同时,系统的磁化率、内能、比热和自由能也呈现出复杂性.     

Improved phenomenological renormalization schemes

An analysis is made of various methods of phenomenological renormalization based on finite-dimensional scaling equations for inverse correlation lengths, the singular part of the free energy density, and their derivatives. The analysis is made using two-dimensional Ising and Potts lattices and the three-dimensional Ising model. Variants of equations for the phenomenological renormalization group are obtained which ensure more rapid convergence than the conventionally used Nightingale phenomenological renormalization scheme. An estimate is obtained for the critical finite-dimensional scaling amplitude of the internal energy in the three-dimensional Ising model. It is shown that the two-dimensional Ising and Potts models contain no finite-dimensional corrections to the internal energy so that the positions of the critical points for these models can be determined exactly from solutions for strips of finite width. It is also found that for the two-dimensional Ising model the scaling finite-dimensional equation for the derivative of the inverse correlation length with respect to temperature gives the exact value of the thermal critical index.     

On limit theorems for the bivariate (magnetization,energy) variable at the critical point

The limiting (magnetization, energy) bivariate variable is studied for Ising ferromagnets at the critical point. The factorization property of the limiting bivariate moment generating function is shown to be intimately connected to critical point exponent inequalities and to the behaviour of the scaling limit near and at the critical point. The validity of this can be deduced from the study of the second and the fourth magnetization cumulants at zero external field. The limiting bivariate variable is exactly calculated at the critical point for the Curie-Weiss model (MF) and for the edge of a two-dimensional Ising ferromagnet wrapped on a cylinder. It is shown that the mean field case leads to a non-Gaussian limiting distribution in contradistinction with the particular Ising model we consider for which we obtain a product of two Gaussian probability distributions.     

Thermodynamic limit for a system with dipole-dipole interactions

The free energy at constant magnetization of a simple cubic lattice of Ising spins with dipole-dipole interactions in periodic boundary conditions is related to the free energy at constant magnetization with no periodicity. The relationship is not one of equality.     

The random field method for the Ising model

The random field method is used for investigation of the Ising model. The generalization of the variational principle and a new representation for the free energy of the Ising model are proposed.     

Magnetization of a Gapped Spin 1/2 Antiferromagnetic Ising Chain near the Critical External Field

We study the magnetization of gapped spin 1/2 XXZ Heisenberg Ising chains and calculate the scattering length among massive spinons. We obtain the magnetization close to the critical external magnetic field. The leading correction term determined by the scattering length among massive spinons is given. Our results are in agreement with exact results and with experimental results. We show that the deviation from the massive free hard core boson picture can be accounted very well by the leading correction term due to the spinon-spinon interaction. We show that the deviation increases along with the increasing of the Ising term.     

Magnetization of a Gapped Spin 1/2 Antiferromagnetic Ising Chain near the Critical External Field

We study the magnetization of gapped spin 1/2 XXZ Heisenberg Ising chains and calculate the scattering length among massive spinons. We obtain the magnetization close to the critical external magnetic field. The leading correction term determined by the scattering length among massive spinons is given. Our results are in agreement with exact results and with experimental results. We show that the deviation from the massive free hard core boson picture can be accounted very well by the leading correction term due to the spinon-spinon interaction. We show that the deviation increases along with the increasing of the Ising term.     

Kac type models of semi-finite spin systems

The Ising model for systems with free surfaces and Kac type interaction is exactly solved. The free energy and the transition point are similar to those obtained for Valenta's model of thin films. The spherical model for the same system is also investigated, and has the same critical temperature.